B Dark matter and Kepler's Law

I keep reading articles that assert that spiral galaxies would fly apart if it were not for the presence of a dark matter halo. The observation that rotational speeds vary little with distance from the center is usually cited as the 'proof' of dark matter since this behavior would otherwise flout Kepler's Law.

But would it? Correct me if I am wrong but doesn't Kepler's Law assume all the mass is at the center of the system? True enough in the case of a star, nowhere near true in a spiral galaxy. Matter near the center would not have to rotate particularly fast to be in a stable orbit around the center because in addition to its own centrifugal force, it is pulled upon by matter further out. The articles are also rather unclear as to the exact whereabouts of the dark matter. If the dark matter resides mostly in the center then one would expect greater adherence to Kepler. If it were mostly at the edge then the rotational speeds would have to slow with distance in excess of Kepler. And if the distribution was roughly akin to the visible matter it would not make any difference to the speed/distance curve surely?

Can anyone explain this or point out articles that give a more complete analysis of mass distribution and rotation?

Whoa! Both very nice documents with a lot to digest, particularly the most recent one. I notice it talks about MOND - a concept I am deeply skeptical of although of course, on galactic scales the expansion of space would begin to creep in as a factor.

Plus the above papers will have to be read in conjunction with other papers on related subjects. In all these dark matter theories, there seems to be profound confidence that we can 'see' all the interstellar gas by looking at the atomic hydrogen lines. I am not sure this confidence is well founded. It would be extremely difficult if not impossible to replicate a reasonable sample of such gas in a laboratory to see if it is as luminous at 21cm as it is presumed. Whilst reasonable calculations can be made about how far photons can penetrate through gas samples we can prepare before being adsorbed and re-emitted, I am not sure how much we know about this might be affected by the proximity of other atoms. Interstellar gas could by much more transparent.

The first paper (eaa-darkmatter-obs.pdf) mentioned 21cm sources beyond where the stars end and said the rotation was flat as far out as the data extended. However it did not say (unless I missed it) - if it got weaker the further out in line with lower levels of light from stars. That there is an end to the region of stars long before there is an end to the region of hydrogen is another mystery in its own right of course.